SOLUTION: if cosx=7/25 ,find tan(x+45)

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Question 1089448: if cosx=7/25 ,find tan(x+45)
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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1.  tan(x+45) = %28tan%28x%29%2Btan%2845%29%29%2F%281-tan%28x%29%2Atan%2845%29%29 = %28tan%28x%29%29%2F%281-tan%28x%29%29.


2.  tan(x) = sin%28x%29%2Fcos%28x%29,

    and since you are just given cos(x) = 7%2F25,  all you need to do is to calculate

    sin(x) = sqrt%281-cos%5E2%28x%29%29 = sqrt%281-%287%2F25%29%5E2%29 = sqrt%281-49%2F625%29 = sqrt%28%28625-49%29%2F625%29 = 24%2F25.


    So, tan(x) = sin%28x%29%2Fcos%28x%29 = %28%2824%2F25%29%29%2F%28%287%2F25%29%29 = 24%2F7.


3.  From this point, can you complete the calculations on your own ??

Solved.